title: Macroscopic response in active nonlinear photonic crystals.
abstract: We derive macroscopic equations of motion for the slowly varying electric field amplitude in three-dimensional active nonlinear optical nanostructures. We show that the microscopic Maxwell equations and polarization dynamics can be simplified to a macroscopic one-dimensional problem in the direction of group velocity. For a three-level active material, we derive the steady-state equations for normal mode frequency, threshold pumping, nonlinear Bloch mode amplitude, and lasing in photonic crystals. Our analytical results accurately recapture the results of exact numerical methods.
authors.forename: Gandhi
authors.initials: G
authors.lastname: Alagappan
authors.forename: Sajeev
authors.initials: S
authors.lastname: John
authors.forename: Er Ping
authors.initials: EP
authors.lastname: Li